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Multiplicative Inverse For numbers, ax = 1 x = 1a x = a –1 xa = 1 What about matrices? A= 12 B = 3 –2 13 –1 1 AB BA We write B = A –1 and never B = 1 A AA –1 = I and A –1A = I Q. What algebraic properties come with the notion of inverse? Q. How does one calculate an inverse if there is one? Zero matrix 0 never has an inverse. Makes sense only for a square matrix. Inverse of A = 1 , don’t even ask. 1 1 Find the inverse of A = 1 2 . 13 Strategy: Find a solution of AX = I 1. Form augmented matrix [A I] 2. Row reduce same 3. See if the row reduced form is [I X]. If so, X = A –1. If not, the matrix doesn’t have an inverse. 2